~ Pergamon Computers md Engng Vol 26, No 2, pp 267-278, 1994 Copyright © 1994 Elsewer Science Ltd 0360-8352(93)E0001-O Pnnted m Great Britain All rights reserved 0360-8352/94 $7 00 + 0 00 LEAD TIME UNCERTAINTY WITH BACK-ORDERING IN MULTI-LEVEL PRODUCT STRUCTURES SURENDRA M.GUPTA* and Louxs BRENNAN Department of Industrial Engmeenng and Information Systems, Northeastern University, Boston, MA 02115, U S A (Recett,ed for pubhcatton 23 November 1993) Abstract--The performance of lot sizing algorithms incorporating back-orders is evaluated and compared with several of the traditional lot sizing rules This comparison is undertaken for a multi-level product structure environment operating under a rolhng horizon in the presence of lead time uncertainty By means of simulation, the impact of a variety of lead t~me scenarios, product structures and cost parameters on lot sizing ~s examined It ~s shown that unlike in the deterministic environment, the back-ordering algorithms can yield superior performance in an uncertain environment INTRODUCTION Back-order lot sizing rules have, until recently, been neglected in the context of MRP. However, of late, there have been a number of developments. For example, a back-order version of the Wagner-Whitln algorithm has been reported which extends the original algorithm [1] to include the possibility of shortages [2]. A computat~onally simpler, yet robust approach to lot sizing with back-orders has since been introduced [3]. This approach referred to as the Gupta-Brennan (G-B) algorithm, was shown to be of comparable performance to Wagner-Whitin with back-orders for single level lot sizing. Furthermore, the performance of the G-B algorithm has been compared with several of the existing traditional lot sizing algorithms as well as the back-order version of the EOQ algorithm (referred to as EQS) in the multi-level product structure environment [4]. It was concluded that the G-B rule is an effective alternatwe If operating constraints dictate back-ordering (e.g. storage space limitations). Thus, a back-ordermg rule, such as G-B, which is computauonally simple and also allows for the nonback-order case, warrants further evaluation in environments which are more consistent with real life conditions. One such condition is the presence of uncertainty. Uncertainty ~mplies that the value under consideration changes from one period to the next and is not known m advance. Uncertain values are d~fficult to cope w~th, because the absence of foreknowledge means that timely recovery of the MRP system is usually impossible. Bahl et al. [5] have recently highlighted the implementation benefits of research directed to complex manufacturing environments involving the two major sources of uncertainty, vtz., demand and supply. Demand uncertainty can arise due to changes, by customers, m the due date specification or in the quantity specified [6]. Additionally, fluctuations in requests for spare parts can gwe rise to demand uncertainty. Likewise, supply uncertainty can arise for a number of reasons. For example, supplier lead times and/or production cycle times could be longer or shorter than planned, the quantity delivered by vendors could be less than the quantity ordered due to hmited avallabdity and at the processing stage the defect rate could be higher than anticipated Very little attention has been given to lead time uncertainty as a research variable in MRP, even though safety stock and safety lead times have been proposed as methods to deal with it [6-8]. Melnyk and Piper [9] studied the effect that choice of lot sizing rule has on lead time error (the difference between the planned and observed lead times) m an MRP system. Grasso and Taylor *Author for correspondence 267